An ovoid of a finite classical polar space is a set of points having exactly one point in common with every generator. An ovoid is a translation ovoid with respect to one of its points if it admits a collineation group fixing all totally isotropic lines through the point and acting regularly on the remaining points of the ovoid. Lunardon and Polverino proved in [11] that Q(+) (3; q), Q (4; q) and Q(+) (5; q) are the only finite orthogonal polar spaces having translation ovoids. In this paper we prove that H (3; q(2)) is the only finite unitary polar space having translation ovoids. We also prove that translation groups of ovoids of H (3; q(2)) contain only linear collineations.
Translation ovoids of unitary polar spaces
SICILIANO, Alessandro
2014-01-01
Abstract
An ovoid of a finite classical polar space is a set of points having exactly one point in common with every generator. An ovoid is a translation ovoid with respect to one of its points if it admits a collineation group fixing all totally isotropic lines through the point and acting regularly on the remaining points of the ovoid. Lunardon and Polverino proved in [11] that Q(+) (3; q), Q (4; q) and Q(+) (5; q) are the only finite orthogonal polar spaces having translation ovoids. In this paper we prove that H (3; q(2)) is the only finite unitary polar space having translation ovoids. We also prove that translation groups of ovoids of H (3; q(2)) contain only linear collineations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
